Using the Lidskii angles in our analysis of the oscillation numbers leads in a natural
way to their connection with the Maslov index of two continuous Lagrangian paths \(Y\) 
and \(\hat{Y}\)  on \([a,b]\) , denoted by \(\operatorname{\text{\rm Mas}}\hspace*{1.0pt}(Y,\hat{Y},[a,b])\) . Here we use the analytic definition
of the Maslov index from [1]}, see also
[2]}, [3]}, [4]}. We show (Theorem REF )
that the Maslov index of \(Y\)  and \(\hat{Y}\)  on \([a,b]\)  can be calculated from the changes
at the endpoints of \([a,b]\)  of the Lidskii angles of the symplectic matrix
\(Z_Y^{-1}(t)\hspace*{1.0pt}Z_{\hat{Y}}(t)\) . This approach is known in
[5]} and [6]}.
Consequently, the Maslov index of \(Y\)  and \(\hat{Y}\)  on \([a,b]\)  is equal to the
oscillation number of the transformed Lagrangian path \(Z_Y^{-1}\hspace*{1.0pt}\hat{Y}\)  on \([a,b]\) , i.e.,
\( \operatorname{\text{\rm Mas}}\hspace*{1.0pt}(Y,\hat{Y},[a,b])={\mathcal {N}}(Z_Y^{-1}\hspace*{1.0pt}\hat{Y},[a,b]),\) 
